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DLMF:15.8.E7 - MaRDI portal

DLMF:15.8.E7 (Q5761)

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DLMF:15.8.E7
No description defined

    Statements

    DLMF defining formula
    F ⁡ ( - m , b c ; z ) = ( c - b ) m ( c ) m ⁢ F ⁡ ( - m , b b - c - m + 1 ; 1 - z ) = ( c - b ) m ( c ) m ⁢ z m ⁢ F ⁡ ( - m , 1 - c - m b - c - m + 1 ; 1 - 1 z ) , Gauss-hypergeometric-F 𝑚 𝑏 𝑐 𝑧 subscript 𝑐 𝑏 𝑚 subscript 𝑐 𝑚 Gauss-hypergeometric-F 𝑚 𝑏 𝑏 𝑐 𝑚 1 1 𝑧 subscript 𝑐 𝑏 𝑚 subscript 𝑐 𝑚 superscript 𝑧 𝑚 Gauss-hypergeometric-F 𝑚 1 𝑐 𝑚 𝑏 𝑐 𝑚 1 1 1 𝑧 {\displaystyle{\displaystyle F\left({-m,b\atop c};z\right)=\frac{(c-b)_{m}}{(c% )_{m}}F\left({-m,b\atop b-c-m+1};1-z\right)=\frac{(c-b)_{m}}{(c)_{m}}z^{m}F% \left({-m,1-c-m\atop b-c-m+1};1-\frac{1}{z}\right),}}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    DLMF defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aadec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1fdec
    0 references
    real or complex parameter
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1fdec
    0 references
    real or complex parameter
    DLMF defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1fdec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C15.S1.XMD9.m1adec
    0 references

    Identifiers

     
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